You are saving for retirement. To live​ comfortably, you decide you will need to save 

​$3 comma 500 comma 0003,500,000 

by the time you are 

6565. 

Today is your 

3131stst 

​birthday, and you​ decide, starting today and continuing on every birthday up to and including your 

6565th 

​birthday, that you will put the same amount into a savings account. If the interest rate is 

7 %7%​, 

how much must you set aside each year to make sure that you will have 

​$3 comma 500 comma 0003,500,000 

in the account on your 

6565th 

​birthday?

Question content area bottom

Part 1

The amount to deposit each year must be 

​$enter your response here.

  ​(Round to the nearest​ cent.)

This problem is about saving money through regular deposits into an account that earns interest. We can approach this using the formula for the **future value of an annuity**. The future value of an annuity formula is given by:

\[
FV = P \times \frac{{(1 + r)^n - 1}}{r}
\]

Where:
- $ FV $ is the future value (in this case, $3,500,000).
- $ P $ is the annual deposit (this is what we want to find).
- $ r $ is the interest rate per period (7% or 0.07 annually).
- $ n $ is the number of periods (from age 31 to 65, so 65 - 31 + 1 = 35 years).

We are given:
- $ FV = 3,500,000 $
- $ r = 0.07 $
- $ n = 35 $

Now, we need to rearrange the formula to solve for $ P $:

\[
P = \frac{FV \times r}{(1 + r)^n - 1}
\]

Let's calculate this now.To accumulate $3,500,000 by your 65th birthday, you must set aside approximately **$25,318.86** each year, starting from your 31st birthday. 

Would you like more details on how this was calculated, or do you have any other questions?

Here are five related questions you might find useful:
1. What happens if the interest rate changes during the saving period?
2. How does the number of years affect the amount you need to save annually?
3. What if you skip some years of deposits? How does that affect your savings goal?
4. How would inflation impact the purchasing power of $3,500,000 in 35 years?
5. Can you achieve the same goal with a different interest rate and fewer years of saving?

**Tip**: Starting early gives compound interest more time to work, which reduces the amount you need to save each year.

You are saving for retirement. To live comfortably, you decide you will need to save $3,500,000 by the time you are 65. Today is your 31st birthday, and you decide, starting today and continuing on every birthday up to and including your 65th birthday, that you will put the same amount into a savings account. If the interest rate is 7%, how much must you set aside each year to make sure that you will have $3,500,000 in the account on your 65th birthday?

Learn how to calculate the annual savings required to reach a retirement goal of $3,500,000 by age 65 with a 7% interest rate. This problem uses the future value of annuities formula and explores key financial mathematics concepts. Suitable for students and professionals learning about savings strategies and compound interest.

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